How would the boiling point change if the atmospheric pressure increases or decreases?

One can think of boiling point as the temperature at which the vapor pressure of the liquid is equal to the pressure exerted by the fluid above it (which we normally term as the atmospheric pressure). This means that if the pressure of the fluid above the liquid is changed, the boiling point changes as well. In other words, if the atmospheric pressure increases over the liquid, its molecules will require more heat to escape to the surroundings and the boiling point of the liquid will be higher. If on the other hand, if the atmospheric pressure were to decrease, liquid molecules would find it easier to escape to the surroundings at a lower temperature and the boiling point of the liquid would be less.

This is the very reason that the boiling point of water falls as we climb mountains.

Hope this helps.